I would like to comment on the paper by Xiang-Dang Xue et al., [1] The bicubic spline technique presented in this paper was first published in a reluctance motor context by Manzer et al., [2].Subsequently, the technique was improved upon by Stephenson and myself in [3].Both of these older papers discuss the more difficult task of fitting to measured data that may contain noise whereas the recent publication only discusses noise-free data. The second paper, in particular, shows how data can be smoothed. For example, to see the smoothing of the fitted surface, contrast Fig. 4 in [3] with (coincidentally) Fig. 4 in [1], the latter shows spurious high-frequency ripples.Also, the bicubic spline technique is well known in mathematical literature and available in standard math libraries (e.g., NAG).Despite the technique being well known in mathematical literature and previously published in the context of reluctance motors, I do not wish to suggest that the authors were in anyway trying to claim the work of others as their own. I would suggest that it was simply an oversight by the authors and that the authors were not aware of either the mathematical literature or motor literature on this subject. Without doubt, bicubic spline is mathematically a mature interpolation technique [2]. The bicubic spline function used in our paper is just based on [2]. Especially, we have pointed out in the last paragraph in Section II in our paper that detailed description of bicubic spline interpolation as seen in [2].
REFERENCESSpline interpolation is widely applicable to science and engineering and is a very efficient tool to precisely fit discrete data. Our paper cited two papers on cubic and bicubic splines in SRM field [3], [4]. In [3], the cubic spline was employed to represent the phase flux linkage/phase current curves for a set of discrete rotor position values. Reference [4] presented that the cubic spline is utilized to fit the experimental data of flux linkage/current and the bicubic spline interpolation is used to estimate the rotor position and the torque.It is clear that our paper has briefly presented previous related works on bicubic spline interpolation in mathematical and SRM fields. The contribution of our paper is 1) to explore how utilizing bicubic spline technique to accurately compute the flux linkage at arbitrary rotor position and current by use of a small quantity of the known data; 2) to investigate the effect of the number and distribution of the known data on the accuracy of the flux linkage interpolation computation; and 3) to apply the bicubic spline interpolation to simulating the SRM drive.It should be noticed that the nonlinear magnetic characteristics in SRM may be obtained from finite-element analysis or experiment on an existing motor, not only from experiment. Furthermore, no measurement noise will exist for finite-element method (FEM). Our paper is focused on accurately and rapidly computing the magnetic characteristics at arbitrary rotor position and current using the bicubic spline technique ...